The present invention generally relates to a method for displaying graphic data by a designated map projection in a digital cartographic system for geographical information processing. More specifically, the present invention is directed to both of a system and a method for varying the displaying map projection by transforming a coordinate value of the graphic data into a desirable map projection.
A method for representing shapes, and ups and downs of a ground surface of the earth is so-called as a map projection (map projection transformations). As the necessary conditions of the map projection, there are such elements: 1 an actual distance being analogously represented on a map (equidistance); 2 an actual area being analogously displayed on a map (equivalence); and 3 an angle at a ground surface being correctly expressed on a map (equiangularity). Since a map drawn on paper is such a fact that a sphere is projected onto a plane, all of the above-described conditions cannot be simultaneously satisfied. To satisfy any of these conditions, a map is represented by a proper map projection, depending upon its usage.
The various sorts of map projections are described in detail in, for instance, Japanese publication entitled "Edition and Projection for Map" written by K. Kosaka, published by SANKAIDO publisher in 1982. In this publication, the calculations for projecting the coordinate systems expressed by longitude and latitude on a spherical surface onto the coordinate systems on a plane, are classified in accordance with shapes of projection surfaces and conditions of projection. There are employed a plane, a cylinder and a conic as the projection planes, whereas the above-described three conditions are handled as the projection conditions.
Conventionally, the coordinate transformation in case that map data are processed in the computer, is handled in view of inputting of a map and calculations of a distance and an area. When a map is inputted, it is necessary to convert a coordinate value of map data which has been written on paper by way of a different map projection, into a common coordinate system in order to totally manage the data. To manage the map data under better matching conditions, it is preferable to employ an expression of a coordinate system based on the longitude and latitude. If the longitude and latitude are utilized, the map data can be continuously managed over an entire region of the earth. In transactions of Japanese System Control Information Institute, "A Geographic Information System REALS for Personal Computer", volume 34, No 5, pages 138-146, 1990 by Taniguchi et al., and "Summary of Country Numeral Information" issued by Japanese Construction Ministry, Geographic map department, map supervision division in 1985, data management based on the longitude and latitude has been performed, In the former publication, there is described such a method for transforming the graphic data into the coordinate system by the longitude and latitude, which have been inputted by the Universal Transverse Mercator coordinate system (UTM coordinate system) employed in a map with a reduction ratio of 1/25000. Since the UTM map projection corresponds to an equiangular projection method, and furthermore a distance can be measured under practically acceptable precision in the map with the medium reduction ratio, there are merits that both the angles and distances can be directly calculated from the coordinate value. As a consequence, the UTM coordinate system has been employed to calculate the distances and areas in the latter publication, and also there is described such a method for transforming the longitude/latitude of the map data into the UTM coordinate system so as to perform this calculation.
Among others, there is another publication "Geographic Information System with Superior Analyzing Function: ARC/INFO" written by Imai, PIXEL, No. 54, pages 65 to 70, 1987 as a digital cartographic system handling a coordinate transformation. This system owns the coordinate transformation function as the edition function during the input/updating operations of the graphic data, and then can execute several different map-projection transformations with respect to the map data.
In case when map data are processed in computers, another map-projection transformation is required in view of output operations other than the above-described input operation. It is difficult to directly judge both azimuth and a distance from the map data which have been totally managed based on the longitude and latitude. While the digital cartographic system is utilized as an information representing means to analyze a region, a proper information representation suitable for a desirable analyzing purpose is required. To achieve an intuitively understandable analysis support, it is required to display map data with satisfying correctness in azimuth as well as correctness in a distance. There are the azimuth map projection and the UTM map projection, functioning as a method for representing either azimuth, or a distance. In accordance with the azimuth map projection used for a plane projection, azimuth at a center point of projection is equal to azimuth at a ground surface, and a line segment for connecting this center line and an arbitrary point, becomes a minimum path between two points. In accordance with the UTM map projection used for the cylindrical-plane projection, an angle between a ground surface and a corresponding map becomes equal, and also a distance on the map can be expressed as being substantially equal to an actual distance under practically acceptable map precision with a medium reduction ratio. However, it is only possible to express continuous coordinate system with having the interval of longitude within a range of 6 degrees in the UTM map projection. As to an area, it is possible to equally express the areas by way of the conical map projection and the cylindrical map projection.
To display map data in various sorts of map projections in conformity to objects, coordinate transforming operations should be carried out at a high speed and also at high precision. Further, when a coordinate system is converted into such a coordinate system as in the UTM coordinate system where discontinuities are present every 6 degrees, the discontinuity should be avoided by a proper way.
First, there is a problem in the coordinate transforming speed. Generally speaking, the coordinate transforming operation for the map data must be carried out with respect to a large quantity of graphic data. In the publication "Edition and Projection of Map", the projection formulae from the longitude and latitude to the coordinate systems of the various map projections are described. Since each of these projection formulae involves trigonometric functions and a logarithm, and therefore requires a large amount of calculating steps, there is a problem that a lengthy calculation time is necessarily required. In particular, since the projection formula to the UTM coordinate system is expressed by a series expanding formula, a back projection is not easily performed, but it is not suitable to calculate a large amount of calculation elements. It should be noted that although the coordinate calculating method with employment of the transforming table between the longitude/latitude and the UTM coordinate system has been described in the above-described publication "Edition and Projection of Map", since this transforming table has a high volume in unit of 1 minute and also the transforming formula is a biquadratic polynomial, a total amount of this calculation is not so reduced. In the publication "Summary of Country Numeral Information", in order to simplify the transformation from the longitude/latitude into the UTM coordinate system, the graphic data are subdivided into segments and one representative point is set in the segment, whereby the transforming formula is analogous to a local formula. Although the calculation of this method may be simplified, there is another problem that shifts happen to occur in the graphic data on the boundary line over the adjoining segments, resulting in an occurrence of discontinuities. Furthermore, the coordinate transformation effected in the ARC/INFO system is intended to perform the editing operation during the input/updating operations of the data, but to convert/display the map projections.
Subsequently, there is a problem in the discontinuities of the graphic data. The UTM map projection is effective to express an angle and a distance. To suppress distortion in the distance, the entire region is subdivided into narrow strips called zones at 6 degrees in this UTM coordinate system. Therefore, as represented in FIG. 8, there are great shifts at a boundary line of the adjoining zones in accordance with the higher latitude, so that the map data are represented with having the discontinuities on this boundary line. To represent the graphic data extending these zones in a continuous form, there is another great problem that such a distortion becomes large in accordance with the higher latitude. It should be noted that the coordinate transformations as defined in the above-described publications "Summary of Country Numeral Information", and "A Geographic Information System REALS for Personal Computer", and intended to effectively manage the data and also correct the analyzing amount, but not to represent various information to users. As a consequence, these coordinate transformation methods still contain the above-described discontinuities in the graphic representations.
In addition thereto, it is necessary to readily produce reference lines such as longitude, latitude and a curve of equal bearing during representation, which own such a function to assist the analysis. Features of the represented map data may be easily grasped by superimposing these reference lines thereon.